Our previous measurements of the in-plane magnetization \(M(H_x)\)  at low \(T\)  (1.8 K) of trigonal EuMg\(_2\) Bi\(_2\)  and EuMg\(_2\) Sb\(_2\) , which is below \(T_{\rm N}\)  of each compound, exhibited positive curvature for \(H_x \lesssim 200\) –500 Oe followed by a proportional behavior up to the respective critical field \(H_{ab}^{\rm c}\)  [1]}, [2]}. Here we formulated a theory which quantitatively explains these results. Due to the threefold trigonal magnetic anisotropy of each compound shown in Fig. REF (a), the A-type AFM ordering leads to three collinear AFM domains at 120\(^\circ \)  to each other. In an applied field \(H_x\)  in the \(ab\)  plane, the ordered moments in each domain rotate with increasing field to become approximately perpendicular to \({\bf H}_x\)  at a critical field \(H_{{\rm c}1}\approx 220\)  Oe for EuMg\(_2\) Sb\(_2\)  and \(\approx 465\)  Oe for EuMg\(_2\) Bi\(_2\)  as illustrated in Fig. REF (b). Then on further increasing \(H_x\) , the moments all tilt towards \({\bf H}_x\)  in such a way that \(M(H_x)\)  is linear in \(H_x\)  as shown in Fig. REF (c) until all moments are parallel to the field at the critical field \(H_{ab}^{\rm c}\)  which is 26 kOe for EuMg\(_2\) Sb\(_2\)  and 27.5 kOe for EuMg\(_2\) Bi\(_2\) .
